PHYSICS 1040L LAB WHEATSTONE BRIDGE Series and
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University of TN Chattanooga Physics 1040L 8/21/2012 PHYSICS 1040L LAB WHEATSTONE BRIDGE SERIES & PARALLEL RESISTANCES Object: To learn how to operate a Wheatstone Bridge and to verify the formulas for the combination of resistances. Apparatus: Slide wire Wheatstone Bridge, decade resistance box, unknown resistors, galvanometer and a battery or power supply. Theory: A Wheatstone Bridge is 4 resistors connected in the form of a square with galvanometer connected across one diagonal and a voltage source across the other, as shown in the circuit below. When the Galvanometer indicates zero current, the bridge is balanced. In this condition, the current, I, branches at A with one part, I B , passing through point B and the remainder, I C , passing through point C. The two parts recombine at point D. Since no current flows through the galvanometer, G, under these conditions, the voltage drop from A to B must be the same as that from A to C. Similarly, the voltage drop from B to D must be the same as that from C to D. Thus: I B R 1 = I C R 4 and I B R 2 = I C R 3 (1) Figure 1: Wheatstone bridge
Transcript of PHYSICS 1040L LAB WHEATSTONE BRIDGE Series and
University of TN Chattanooga Physics 1040L 8/21/2012
PHYSICS 1040L LAB WHEATSTONE BRIDGE SERIES & PARALLEL RESISTANCES Object: To learn how to operate a Wheatstone Bridge and to verify the formulas for the combination of resistances. Apparatus: Slide wire Wheatstone Bridge, decade resistance box, unknown resistors, galvanometer and a battery or power supply. Theory: A Wheatstone Bridge is 4 resistors connected in the form of a square with galvanometer connected across one diagonal and a voltage source across the other, as shown in the circuit below. When the Galvanometer indicates zero current, the bridge is balanced. In this condition, the current, I, branches at A with one part, IB, passing through point B and the remainder, IC, passing through point C. The two parts recombine at point D. Since no current flows through the galvanometer, G, under these conditions, the voltage drop from A to B must be the same as that from A to C. Similarly, the voltage drop from B to D must be the same as that from C to D. Thus:
IBR1 = ICR4 and IBR2 = ICR3 (1)
Figure 1: Wheatstone bridge
University of TN Chattanooga Physics 1040L 8/21/2012
R1 /R2 = R4 /R3 or R1 R3 = R4 R2 (2) In practice, only one resistance is unknown and the others are known and variable. In the slide wire Wheatstone Bridge, two of the resistances are the two ends of the wire divided by the sliding contact. (See Fig 2)
Figure 2: CENCO Metal Slide Wire Wheatstone Bridge. May come in other colors or made out of wood.
In the diagram, the slide wire is represented by R4 and R3, and the sliding contact is the point C. Since the resistance per unit length of the slide wire is constant, the length of the two ends of the slide wire, L4 and L3, may be substituted for R4 and R3, respectively. If, also, an unknown resistor, Xn, is inserted in place of R1, and a standard resistor, RS, inserted in place of R2, the above expression may be written:
Xn = RS (L4 / L3). (3)
University of TN Chattanooga Physics 1040L 8/21/2012
Fig. 3: Bridge For Determining Unknown Resistance
Figure 4: Sliding Contact Switch on CENCO Bridge.
University of TN Chattanooga Physics 1040L 8/21/2012
Figure 5: Left end of bridge.
Figure 6: Right end of bridge
University of TN Chattanooga Physics 1040L 8/21/2012
Figure 7: Xn Unknown Resistor Board
Figure 8: Rs DECADE RESISTANCE BOX
University of TN Chattanooga Physics 1040L 8/21/2012
Fig. 9 Physical Layout Of Circuit
Figure 10: Galvanometer
University of TN Chattanooga Physics 1040L 8/21/2012
Figure 11: Power Supply
Procedure and Data Analysis
1. Choose resistors R1, R2, and R3 from your unknown resistors board and record their labels. Note you must use 3 resistors (Your choice from resistors B, C, D, and E) for resistors R1, R2, and R3. DO NOT USE RESISTORS A OR F.
2. The approximate values of B, C, D, E, are 10, 50,120 and 500 Ω, Ω, Ω, Ω, BUT NOT IN ANY PARTICULAR ORDER
3. Connect the circuit as shown in Fig 9. You may look at your data page for a
simplified drawing of the circuit. Use resistor R1 for THE FIRST unknown resistor.
4. You MUST make sure to always keep the resistance Rs on the decade resistance box set to at least 10 or 20 Ohms at all times. Never set it to zero!
5. Position the sliding contact on the ruler between 0.4 and 0.6 m
6. Set the decade resistance box to one of the resistances listed above. You are using the decade resistance box as your course adjustment.
7. Now touch the contact switch to the wire.
8. Is the galvanometer any where the Zero point on the scale?
University of TN Chattanooga Physics 1040L 8/21/2012
9. If it is, adjust the slide wire contact switch back and forth between 0.4 and 0.6 m. until the galvanometer reads Zero.
10. If the galvanometer does not read Zero at any point where you touch the contact switch to the wire, it usually means that Rs is not adjusted to the approximate value of the unknown resistor.
11. Change the value of Rs and try to balance the circuit again.
12. When the circuit is balanced, temporarily disconnect the Decade Resistance Box from the circuit by unplugging the Banana Plug wires.
13. Measure the resistance of Rs using the Ohmmeter setting of the multimeter. The Ohmmeter setting has the Greek letter Ω next to it.
14. Plug the Decade Resistance box back into the circuit.
15. Record your data for the length and RS.
16. Repeat the steps 5 -15 for R2 and R3 .
17. Connect R1, R2, and R3 in series (see diagram on your data page and below). Repeat steps 5 - 15 with the series combination.
18. Connect R1, R2, and R3 in parallel (see diagram on your data page and below) Repeat steps 5 - 15 with the parallel combination.
19. Calculate the equivalent resistance for the series connection from the individual measurements of R1, R2, and R3. Find the percent difference between the measured and calculated values.
20. Calculate the equivalent resistance for the parallel connection from individual measurements of R1, R2, and R3. Find the percent difference between the measured and calculated values.
21. In your report do not forget to show examples of all calculations, use proper units, round the answers, and make a conclusion about your findings.
University of TN Chattanooga Physics 1040L 8/21/2012
Figure 12: Example of a Series connection on resistor board. Yours might not look exactly like this.
Figure 13: Example of a parallel connection. Yours might not look exactly like this.
University of TN Chattanooga Physics 1040L 8/21/2012
